We still haven't explained why, despite all this branching, our minds keep insisting on having had a single past (they also think they have a single future, but this can be dismissed as wishful thinking). In fact, not only do we have memories of a single past, but also our environment mostly corroborates these memories.
But there are actually infinitely many histories that could have generated our memories, both external and internal. At the macro level, if entropy destroys information about some event, we can't be sure which version of this event actually took place. At the micro level, we have the uncertainty principle—we can't tell exactly from where a certain particle arrived because we can't measure its exact position and speed at the same time.
But the question of time, in particular the distinction between the past and the future, is still subtler. It is known that QFT is symmetric with respect to the reversal of time (more precisely, the so called CPT—charge, parity, time—invariance requires the inversion of charges and parity to accompany the reversal of time). Feynman diagrams can be used in essentially the same way to "predict" the past as they predict the future. In fact, predicting the future makes little sense in the Metaverse where all possibilities are always realized.
And this brings us back to our earlier question about the meaning of probability in the context of the many-universe theory. Let me formulate this question somewhat differently: "How is it that we seem to remember that the outcomes of our experiments fell more often in the high-probability area than in the low-probability area?" I'm not talking here about predicting the future but rather of analyzing the past. We don't know what the future will bring, so calculating future probabilities is just a speculation. Future probability doesn't tell us anything. In fact, it tells us that all possibilities are possible, so the future can't really surprise us. Even if the most unlikely thing happens, e.g., we win a lottery; it won't disprove our earlier calculations of the minuscule odds of that event. On the other hand, when we statistically analyze the outcomes of previous experiments, we see probability at work. (We then often use the principle of induction to apply these results to the prediction of future outcomes of similar experiments.)
So let's forget about predicting future probabilities and concentrate on calculating past probabilities. Given a certain state of the present—and that includes our memories, written records, positions of objects around us, etc.—we can deduce what our past was. We do this deduction every time we retrieve our internal memory or observe an external event. Imagine, for instance, that you see a pencil falling off the table. What it means, is that some photons brought the image of a falling pencil to your retina, which reacted by transforming them into electrical signals, which through the optic nerve arrived at your brain, where they registered as "an image of a falling pencil." How sure are you that the pencil actually fell? After all, there is a non-zero probability that the photons coming from around the table exchanged some virtual electron-positron pairs with each other and with the background radiation, which changed their paths in such a way that they formed a fake picture of a falling pencil on your retina. Granted, the probability of such an event is so tiny that it makes no sense to even think about it.
But wait! We have just applied a probability argument to the past. We assumed that the most probable past actually happened, whereas, from the point of view of the Metaverse, both pasts are there along with a myriad of other less probable pasts. Given the choice, we selected the one with the highest probability as our "real" past. In most cases, when you have a memory of some event plus a lot of corroborating evidence, the past that contained that event is by far the most probable. That's why we have such a strong conviction that there was only one past history.
Finally, let us address the question of the arrow of time. Why, despite the time-reversal (CPT) symmetry of QFT, does there seem to be a fundamental difference between the past and the future? There is one theory in Physics that is not invariant with respect to time reversal: Thermodynamics. One of the axioms of Thermodynamics is that the entropy (the measure of disorder) of an isolated system can only increase with time and never decrease. So the ratchet of entropy can serve as a determinant of the arrow of time. Future is where the entropy is higher and past is where it's lower. How can we then reconcile QFT with Thermodynamics?
The first thing to note about Thermodynamics is that it deals with probabilities. The entropy of a system may theoretically decrease, but such an event is very unlikely. (The larger the system, the more unlikely it is.) In the Metaverse, probability has no meaning—There are futures with higher entropy and futures with lower entropy. What happens is that we call the futures with lower entropy "pasts." In each classical neighborhood we can establish the arrow of time by looking at the direction of the change in entropy. For some neighborhoods, the arrow will point in one direction, for others in the opposite direction. The invariance of QFT tells us that there are as many "forward" neighborhoods as there are "backward" neighborhoods. We can even speculate that there is some continuity of the arrow of time from point to point. In fact that's how we could interpret the laws of Thermodynamics: It is very unlikely that the arrow of time will get reversed along a classical path.